Barclays chief executive Bob Diamond is facing calls to resign over a scandal in which the bank's traders tried to manipulate the interest rates at which banks lend to one another.
Former RBS chair Sir George Matthewson told the Today programme that the behaviour of the individual traders involved was "appalling".
If senior management knew what was going on, he said, then "they deserve everything they are going to get".
"Bob Diamond is the first chief executive to command the sort of rewards he is getting, there is a very high expectation of him," he told John Humphrys.
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